On heat kernel estimates and parabolic Harnack inequality for jump processes on metric measure spaces

Acta Mathematica Sinica, English Series

Volumn 25, Issue 7, 2009, Pages 1067-1086

  Chen, Zhen Qing ^a,b   Kim, Panki ^c   Kumagai, Takashi ^d  

^a UNIVERSITY OF WASHINGTON   (United States)

^b BEIJING INSTITUTE OF TECHNOLOGY   (China)

^c Seoul National University   (South Korea)

^d KYOTO UNIVERSITY   (Japan)

Author keywords

Dirichlet form; Heat kernel estimates; Jump process; Jumping kernel; Parabolic Harnack inequality

Indexed keywords

EID: 77952861303     PISSN: 14398516     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10114-009-8576-7     Document Type: Article

References (9)

1. Chen, Z.-Q., Kumagai, T.: Heat kernel estimates for jump processes of mixed types on metric measure spaces. Probab. Theory Relat. Fields, 140, 277-317 (2008).
2. Chen, Z.-Q., Kim, P., Kumagai, T.: Weighted Poincaré inequality and heat kernel estimates for finite range jump processes. Math. Ann., 342(4), 833-883 (2008).
3. Barlow, M. T., Bass, R. F., Kumagai. T.: Parabolic Harnack inequality and heat kernel estimates for random walks with long range jumps. Math. Z., 261, 297-320 (2009).
4. Chen, Z.-Q., Kumagai. T.: Heat kernel estimates for stable-like processes on d-sets. Stochastic Process Appl., 108, 27-62 (2003).
5. Hu, J., Kumagai, T.: Nash-type inequalities and heat kernels for non-local Dirichlet forms. Kyushu J. Math., 60, 245-265 (2006).
6. Fukushima, M., Oshima, Y., Takeda, M.: Dirichlet Forms and Symmetric Markov Processes, de Gruyter, Berlin, 1994.
7. Masamune, J., Uemura, T.: Consevative property of symmetric jump processes. Preprint, 2008.
8. Barlow, M. T., Bass, R. F., Chen, Z.-Q., Kassmann, M.: Non-local Dirichlet forms and symmetric jump processes. To appear in Trans. Amer. Math. Soc., 361, 1963-1999 (2009).
9. Barlow, M. T., Grigor'yan, A., Kumagai, T.: Heat kernel upper bounds for jump processes and the first exit time. To appear in J. Reine Angew. Math., 626, 135-157 (2009).